Tropical TCV as a process diagnostic: connecting probability to convective processes in km-scale models via moisture budget statistics

Observations show a bimodal frequency distribution in total column vapour (TCV) over tropical oceans, with convective rainfall predominantly produced on the moist side of the frequency minimum between two modal peaks. Here we show a km-scale model of the tropics with explicit convection produces a bimodal TCV distribution, whereas the same model with parameterized convection does not. The parameterized model also fails to realistically confine rainfall to a moist mode. Using concepts from statistical mechanics we relate TCV frequency and tendency, and isolate process contributions to tendency in TCV phase-space. Where bimodality is lacking, we find an incorrect relationship between moisture flux convergence and TCV in environments with little or no rainfall. The resulting lack of a strong gradient in TCV tendency with respect to TCV is inconsistent with that expected to maintain a TCV frequency minimum.  Our results demonstrate value in the TCV probability distribution as a process diagnostic for the upscale impacts of convection, and as a test for realism in model moisture-dynamics coupling.